Law of Large Numbers (LLN) and Central Limit Theorem (CTL)
30th June 2015
Law of Large Numbers (LLN) and Central Limit Theorem (CTL)
Law of Large Numbers (LLN)
Definition
Be \(X_1, X_2, ...\) random variables with finite variances and be \(S_n = X_1+X_2+...+X_n\). The sequence \({X_n:n\geq1}\) satisfies the Law of Large Numbers if:
Be \({X_n:n\geq1}\) independent random variables, identically distributed and with expected value \(\mu\) and variance \(\sigma^2\), with \(0<\sigma^2<\infty\). For \(S_n=X_1+X_2+...+X_n\),